Published Paper

Inserted: 3 dec 2013
Last Updated: 21 apr 2018

Journal: SIAM Numer. Anal.
Year: 2013

Abstract:

We consider the multiphase shape optimization problem

$\min\Big\{\sum_{i=1}^h\big(\lambda_1(\Omega_i)+c \vert
\Omega_i \vert
\big):\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset \Big\},$

where $c>0$ is a given constant and $D\subset\mathbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide some numerical results for the optimal configuration.

Keywords: monotonicity formula, shape optimization, eigenvalues, multiphase, optimal partition

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